Sound Synthesis of the Harpsichord Using a Computationally Efficient Physical Model

Vesa Välimäki¹, Henri Penttinen¹, Jonte Knif², Mikael Laurson², and Cumhur Erkut¹

¹Helsinki University of Technology, Laboratory of Acoustics and Audio Signal Processing, Espoo, Finland
²Sibelius Academy, Centre for Music and Technology, Helsinki, Finland

This is a companion web page to a paper with the same title that was published in the EURASIP Journal on Applied Signal Processing (special issue on Model-Based Sound Synthesis) in June 2004 (issue 7, pp. 934-948). The full version of the paper is available online (for everybody!) here.

ABSTRACT

A sound synthesis algorithm for the harpsichord has been developed by applying the principles of digital waveguide modeling. A modification of the commuted waveguide synthesis approach is used, where each tone is generated with a parallel combination of a string model and a resonator that are excited with a common excitation signal. The parallel resonator is used, as proposed previously, to reproduce the beating effect appearing in many harpsichord tones. A modification to the loss filter of the string model is introduced which allows more flexible control of decay rates of partials than a typically used first-order filter. The characteristic thump terminating tones played with the harpsichord is reproduced by triggering a sample that has been extracted from a recording. A digital filter model for the soundboard has been designed based on recorded bridge impulse responses of the harpsichord. The output of the string models is injected in the soundboard filter that imitates the reverberant nature of the soundbox and particularly the ringing of the short parts of the strings behind the bridge.

Keywords: acoustic signal processing, computer music, digital filter design, digital signal processing, digital waveguide modeling, electronic music, musical acoustics, physical modeling of musical instruments, sound synthesis

Sound examples related to this work

Example of the sound of the instrument recorded this study.

Funky harpsichord recording (WAV, 1.7 MB)

The basic Karplus–Strong algorithm produces sounds that are reminiscent of the harpsichord for many listeners, but only when a high sample rate is used. This synthesis technique has been shown to be a simplified version of the waveguide string model that is extensively used for synthesis of stringed instruments and that we use in this work.

Four octaves of C major scale synthesized with the basic Karplus-Strong plucked-string algorithm (WAV, 600 kB). The sampling rate is 44100 Hz. No attempt is made to imitate any particular string instrument. The input signal (initial content of the wavetable) is a white noise sequence (i.e., random numbers with uniform distribution between -1 and 1).

Our synthesizer uses two sample databases, one for the excitation signals and another for release sounds.

Excitation signals for three different keys played twice (WAV, 491 kB)
A key release sample, twice (WAV, 425 kB)

The ripple filter inserted in the loop of the string model enables interesting timbral variations. It allows large deviations in the decay rate of different harmonics.

Two synthetic tones whose parameters are otherwise the same, but for the second tone the ripple filter parameters are adjusted so that the tenth harmonic decays very slowly. These signals were generated with the Karplus-Strong algorithm with the ripple filter. (WAV file, 444 kB)

In the synthesis model, the response of the soundboard is imitated with a reverberation algorithm, which is similar to those used for simulating room reverberation. The soundbox can be interpreted to be a very small room.

Acoustic response of the harpsichord soundboard excited with an impulse hammer (WAV, 569 kb)
Impulse response of the reverberation algorithm that is tuned to simulate the above soundboard response (WAV, 567 kb)

The ringy characteristics of the soundbox response are partly caused by the short ends of the strings behind the bridge. They are not ideally damped, and they produce a faint bell-like sound, when the instrument is played.

Short string ends excited by plucking (WAV, 641 kB)

The effect brought about by the soundbox reverberation algorithm is heard clearly in staccato tones. Compare the following two synthetic examples:

Staccato tones without the soundbox reverb (MP3, 81 kB)
Staccato tones with the soundbox reverb (MP3, 80 kB)

Compare also the following two synthetic examples:

A cadence without the soundbox reverb (MP3, 146 kB)
A cadence with the soundbox reverb (MP3, 146 kB)

Finally, listen to the following short piece of baroque music played on the harpsichord synthesizer: J. J. Froberger, Gigue, A minor, Suite no. 30 (46 sec, MP3, 558 kB).

Sound Synthesis of the Harpsichord Using a Computationally Efficient Physical Model

Vesa Välimäki1, Henri Penttinen1, Jonte Knif2, Mikael Laurson2, and Cumhur Erkut1

This is a companion web page to a paper with the same title that was published in the EURASIP Journal on Applied Signal Processing (special issue on Model-Based Sound Synthesis) in June 2004 (issue 7, pp. 934-948). The full version of the paper is available online (for everybody!) here.

ABSTRACT

Sound examples related to this work

Links

Vesa Välimäki¹, Henri Penttinen¹, Jonte Knif², Mikael Laurson², and Cumhur Erkut¹